Kinetics of a Rigid Body

Abstract

We start by discussing Euler’s laws for a rigid body. These laws are known as the balances of linear and angular momenta. An alternative form of these laws is also presented that is useful for solving problems. We then discuss the kinetic energy of a rigid body and establish the Koenig decomposition. This decomposition, combined with the balance laws, can be used to prove a work-energy theorem for a rigid body. As illustrations of the theory we consider four classes of problems: purely translational motion of a rigid body, rigid bodies that are free to rotate about one of their fixed material points, rolling and sliding bodies, and an imbalanced rotor problem. These applications are far from exhaustive, but we feel they are the chief representatives of problems for an undergraduate engineering dynamics course.